1. Field of the Invention
The present invention relates to an image interpolation apparatus which can minimize degradation of a spatial resolution caused by interpolation performed when an image is enlarged/reduced by affine transformation or the like.
2. Description of the Related Art
As an example of affine transformation, an image enlarging/reducing is performed. Enlargement of an image by means of affine transformation is performed as in the following two cases: a case wherein, as shown in FIG. 1, the display size of an image is not changed but the number of pixels (each represented by a square) is increased with respect to an original image (in this case, the display size of each pixel is reduced); and another case wherein, as shown in FIG. 2, both the display size of an image and the number of pixels are increased (in this case, the display size of each pixel is not changed). New pixel data generated by enlargement processing (affine transformation) is obtained from the pixel data of an original image data by interpolation. When reduction of an image is to be performed, interpolation is also performed.
Such interpolation includes 0th-order (nearest neighbor) interpolation, 1st-order interpolation (linear interpolation), higher-order (3rd, 5th, 7th, . . . ) interpolation, Lagrange's interpolation, spline interpolation, and sinc interpolation. Linear interpolation advantageously allows simple processing. An advantage of higher-order interpolation, e.g., sinc interpolation is that high-precision processing can be performed.
Linear interpolation in which a number of pixels of the image is increased four times will be described below with reference to FIG. 3. Referring to FIG. 3, four pixel data of an original image shown on the left side are respectively denoted by reference symbols a to d. Assume that the original image is subjected to affine transformation to increase the number of pixels four times without changing the display size in the same manner as described with reference to FIG. 1, and an enlarged image shown on the left side in FIG. 3 is obtained. In the enlarged image, pixel data between the pixels a and c is interpolated as (a+c)/2 on the basis of the two pixel data. Similarly, pixel data between the pixels c and d is interpolated as (c+d)/2; pixel data between the pixels b and d, as (b+d)/2; pixel data between a and b, as (a+b)/2; and pixel data in the center of the pixels a, b, c, and d, as (a+b+c+d)/4. Pixels indicated by hatched portions in FIG. 3 are respectively interpolated by using adjacent pixels in the vertical and horizontal directions. In sinc interpolation, new pixels of an enlarged image are interpolated by means of a convolution integration of sinc function and surrounding pixels of the original image.
Linear interpolation and sinc interpolation can be considered as filter processing. Degradation of a modulation transfer function characteristic (to be referred to as an MTF characteristic hereinafter) by an interpolation filter will be described below. FIG. 4A shows an MTF characteristic M.sub.O in an original image. FIG. 4B shows the MTF characteristic of an affine transformation circuit (interpolation filter), in which a characteristic H.sub.L is obtained by linear interpolation and a characteristic H.sub.S is obtained by sinc interpolation. As indicated in FIG. 4B, the MTF characteristic H.sub.L of the linear filter exhibits a low-pass filter characteristic in which a high-frequency gain is degraded, whereas the MTF characteristic H.sub.S of the sinc interpolation filter exhibits a frequency characteristic in which a gain is kept constant and not changed from a zero frequency to a Nyquist frequency fn. For this reason, an MTF characteristic M.sub.S ' of an image upon affine transformation using the sinc interpolation filter is substantially the same as the MTF characteristic M.sub.O of the original image, as shown in FIG. 4C. However, an MTF characteristic M.sub.L ' of an image upon affine transformation using the linear interpolation filter exhibits degradation in a high-frequency range due to the low-pass filter effect.
The degradation of the MTF characteristic in the high-frequency range causes degradation of the spatial resolution of an image. For this reason, if the display size of an image is enlarged by affine transformation using the linear interpolation filter so as to perform diagnosis of details, the image is defocused and the diagnosis of details is difficult to perform. In affine transformation using the sinc interpolation filter, although degradation of a spatial resolution can be prevented, the processing time for interpolation is 10 or more times longer than that in affine transformation using the linear interpolation filter. As described above, in the conventional interpolation techniques for enlargement of images, simple linear interpolation results in poor spatial resolution, and if sinc interpolation is performed to improve the spatial resolution, the processing time is greatly prolonged. This equally applies to reduction of images and to other interpolation processing for enlargement/reduction of images other than affine transformation.